In triangle ABC, angle C is 90º, sin A = 0.6; AC = 12. Find AB.

A triangle is three points that do not lie on one straight line, connected by segments. In this case, the points are called the vertices of the triangle, and the segments are called its sides.

A triangle in which one angle is 90º is called rectangular.

Since, according to the condition of the problem, we only know the length of the leg AC adjacent to the angle A, in order to calculate the length of the hypotenuse AB, only the cosine theorem can be applied. The cosine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse:

cos A = AC / AB;

AB = AC / cos A.

For this we find cos A. Since the sine of the angle A is 0.6, then its degree measure is 37º. The cosine of 37º is 0.8.

AB = 12 / 0.8 = 15 cm.

Answer: the length of the hypotenuse AB is 15 cm.